Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Question 20
![Differentiate each function in Problems 5 to 8 with respect
to the given variable of the function.
YA
8-
5. а. g(u) — и5
= us
b. u(x) — Зх — 1
X
с. f(x) %3D (3х — 1)5
6. а. g(и)
8-
-4
4
— из
-4
b. и(х) — х? +1
8-
c. f(x) = (x² + 1)³
7. а. g(u) — и15
b. u(x) — Зх? + 5х — 7
с. f(x) — (3x2+5х — 7)15
8. а. g(u) — и"
b. u(х) — 5 -8х —12х2
Figure 3.12 Functions y = f(x) (red) and y = g(x) (blue).
d
d
а. Find
f[g(x)]|-2 b. Find g[f(x)],-2
dx
dx
-
27. The graphs of u = g(x) and y
Figure 3.13.
= f(u) are shown in
с. f(х) — (5 — 8х — 12х?)7
-
.
YA
Differentiate each function in Problems 9 to 18.
9. у %3D (5 — х +x*)°
10. y = e2+x²
-
4
1
11. y =
12. y = e(x+1)"
(1+x – x5)12
2-
13. y = In x2
14. y = (2x + 12)"
4
15. y = In(2x +5)
16. у — хе-*
y = f(u)
U =
17. y = (x* – 1)10(2x+ + 3)7
18. у
4 – x2
Figure 3.13 Chain rule with graphs.
Find dy/dx by implicit differentiation in Problems 19
a. Find the approximate value of u at x = 2. What is
the slope of the tangent line at that point?
to 25.
19. x² + y = x³ + y°
b. Find the approximate value of y at x = 5. What is
the slope of the tangent line at that point?
c. Find the slope of y
20. xy = 25
ху
21. xy(2x + 3y) = 2
f[g(x)] at x = 2.
to
4.
6)
6.
4-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4db1e84-75df-498d-9686-5cabfd0e0c2f%2F266396ee-ec14-4b6f-b7c9-ec4f5026f816%2F66hnyl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Differentiate each function in Problems 5 to 8 with respect
to the given variable of the function.
YA
8-
5. а. g(u) — и5
= us
b. u(x) — Зх — 1
X
с. f(x) %3D (3х — 1)5
6. а. g(и)
8-
-4
4
— из
-4
b. и(х) — х? +1
8-
c. f(x) = (x² + 1)³
7. а. g(u) — и15
b. u(x) — Зх? + 5х — 7
с. f(x) — (3x2+5х — 7)15
8. а. g(u) — и"
b. u(х) — 5 -8х —12х2
Figure 3.12 Functions y = f(x) (red) and y = g(x) (blue).
d
d
а. Find
f[g(x)]|-2 b. Find g[f(x)],-2
dx
dx
-
27. The graphs of u = g(x) and y
Figure 3.13.
= f(u) are shown in
с. f(х) — (5 — 8х — 12х?)7
-
.
YA
Differentiate each function in Problems 9 to 18.
9. у %3D (5 — х +x*)°
10. y = e2+x²
-
4
1
11. y =
12. y = e(x+1)"
(1+x – x5)12
2-
13. y = In x2
14. y = (2x + 12)"
4
15. y = In(2x +5)
16. у — хе-*
y = f(u)
U =
17. y = (x* – 1)10(2x+ + 3)7
18. у
4 – x2
Figure 3.13 Chain rule with graphs.
Find dy/dx by implicit differentiation in Problems 19
a. Find the approximate value of u at x = 2. What is
the slope of the tangent line at that point?
to 25.
19. x² + y = x³ + y°
b. Find the approximate value of y at x = 5. What is
the slope of the tangent line at that point?
c. Find the slope of y
20. xy = 25
ху
21. xy(2x + 3y) = 2
f[g(x)] at x = 2.
to
4.
6)
6.
4-
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning